COM S 687 Introduction to Cryptography October 19, 2006


 Rafe Matthews
 1 years ago
 Views:
Transcription
1 COM S 687 Introduction to Cryptography October 19, 2006 Lecture 16: NonMalleability and Public Key Encryption Lecturer: Rafael Pass Scribe: Michael George 1 NonMalleability Until this point we have discussed encryptions that prevent a passive attacker from discovering any information about messages that are sent. In some situations, however, we may want to prevent an attacker from creating a new message from a given encryption. Consider an auction for example. Suppose the Bidder Bob is trying to send a message containing his bid to the Auctioneer Alice. Private key encryption could prevent an attacker Eve from knowing what Bob bids, but if she could construct a message that contained one more than Bob s bid, then she could win the auction. We say that an encryption scheme that prevents these kinds of attacks is nonmalleable. Informally, if a scheme is nonmalleable, then it is impossible to output an encrypted message containing any function of a given encrypted message. Formally, we have the following definition: Definition 1 (NonMalleability) Let (Gen, Enc, Dec) be an encryption scheme. Let NM(m, A) be the output of the following experiment: 1. k Gen(1 m ) 2. c Enc k (m) 3. c 1, c 2, c 3,..., c l A(c, 1 m ) 4. m i if c i = c and Dec k (c i ) otherwise 5. output (m 1, m 2,...,m l ) Then (Gen, Enc, Dec) is nonmalleable if for every nonuniform PPT A, and for every nonuniform PPT D, there exists a negligible ǫ such that for all m 0, m 1 {0, 1} n, Pr [D(NM(m 0, A)) = 1] Pr [D(NM(m 1, A)) = 1] ǫ(n) One nontrivial aspect of this definition is the conversion to of queries that have already been made (step 4). Clearly without this, the definition would be trivially unsatisfiable, because the attacker could simply forge the encryptions that they have already seen by replaying them. 161
2 1.1 Relation Based NonMalleability We chose this definition because it mirrors our definition of secrecy in a satisfying way. However, an earlier and arguably more natural definition can be given by formalizing the intuitive notion that the attacker cannot output an encryption of a message that is related to a given message. For example, we might consider the relation R next (x) = {x + 1}, or the relation R withinone (x) = {x 1, x, x + 1}. We want to ensure that the encryption of x doesn t help the attacker encrypt an element of R(x). Formally: Definition 2 (Relation Based NonMalleability) We say that an encryption scheme (Gen, Enc, Dec) is relation based nonmalleable if for every PPT adversary A there exists a PPT simulator S such that for all PPTrecognizable relations R, there exists a negligible ǫ such that for all m M with m = n, and for all z, it holds that Pr[NM(A(z), m) R(m)] Pr[k Gen(1 n ); c S(1 n, z); m = Dec k (c) : m R(m)] where i ranges from 1 to a polynomial of n and NM is defined as above. This definition is equivalent to the nonrelational definition given above. < ǫ Theorem 1 (Enc, Dec, Gen) is a nonmalleable encryption scheme if and only if it is a relationbased nonmalleable encryption scheme. Proof. ( ) Assume that the scheme is nonmalleable by the first definition. For any given adversary A, we need to produce a simulator S that hits any given relation R as often as A does. Let S be the machine that performs the first 3 steps of NM(A(z), m ) and outputs the sequence of cyphertexts, and let D be the distinguisher for the relation R. Then Pr[NM(A(z), m) R(m)] Pr[k Gen(1 n ); c S(1 n, z); m = Dec k (c) : m R(m)] = Pr[D(NM(A(z), m))] Pr[D(NM(A(z), m ))] ǫ as required. ( ) Now, assume that the scheme is relationbased nonmalleable. Given an adversary A, we know there exists a simulator S that outputs related encryptions as well as A does. The relationbased definition tells us that NM(A(z), m 0 ) Dec(S()) and Dec(S()) NM(A(z), m 1 ). Thus, by the polynomial jump lemma, NM(A(z), m 0 ) NM(A(z), m 1 ) which is the first definition of nonmalleability. 162
3 1.2 NonMalleability and Secrecy Note that nonmalleability is a distinct concept from secrecy. For example, onetime pad is perfectly secret, yet is not nonmalleable (since one can easily produce the encryption of a b give then encryption of a, for example). However, if we consider CCA2 attacks, then the two definitions coincide. Theorem 2 An encryption scheme Σ = (Enc, Dec, Gen) is CCA2 secret if and only if it is CCA2 nonmalleable Proof sketch. If Σ is not CCA2 nonmalleable, then a CCA2 attacker can break secrecy by changing the provided encryption into a related encryption, using the decryption oracle on the related message, and then distinguishing the unencrypted related messages. Similarly, if Σ is not CCA2 secret, then a CCA2 attacker can break nonmalleability by simply decrypting the cyphertext, applying a function, and then reencrypting the modified message. 2 Public Key Encryption Thus far we have considered private key encryption schemes where the encrypter and the decrypter share a common secret. This means that they are forced to meet in advance and agree on a secret. Ideally, we would like to drop this requirement. At first blush this seems impossible. Certainly the decryptor needs a key or else there is nothing preventing an attacker from doing the same thing that the decryptor does. Moreover, the encryptor needs the key because otherwise the key cannot help to decrypt the cyphertext. The flaw in this argument is that there is no need for the encrypter and the decryptor to have the same key, and in fact this is how public key cryptography works. We split the key into a secret decryption key S k and a public encryption key P k. The public key is published in a secure repository, where anyone can use it to encrypt messages. The private key is kept by the recipient, so that only she can decrypt. We define a public key encryption scheme as follows: Definition 3 (public key encryption scheme) A triple (Gen, Enc, Dec) is a public key encryption scheme over a message space M if 1. Gen is a PPT that outputs a pair P k, S k 2. Enc is a PPT that given P k and m produces a cyphertext c 163
4 3. Dec is a PPT that given c and S k produces a message m 4. For all m M and for all p k, s k Gen(1 k ), Dec Sk (Enc Pk (m)) = m Definition 4 (Secure PK Encryption) We say that a public key encryption scheme is secure if for every nonuniform PPT A, there exists a negligible ǫ such that for all messages m 0 and m 1 with m 0 = m 1, it holds that Pr[P k, S k Gen(1 n ) : A(P k, Enc Pk (m 0 )) = 1] Pr[P k, S k Gen(1 n ) : A(P k, Enc Pk (m 1 )) = 1] ǫ These definitions can be extended in a straightforward manner to get appropriate definitions for CPA security, as well as CCA1 and CCA2 security. Since the public key is available to the attacker, CPA security comes almost for free, but CCA1 and CCA2 secure schemes are much harder to come by. With these definitions, there are some immediate impossibility results: perfect secrecy it is clearly impossible to do perfect publickey secrecy, since an unbounded adversary could simply encrypt every message with every random string and lookup the cyphertext deterministic encryption it is impossible to have a deterministic encryption algorithm, because with a deterministic encryption algorithm, the encrypt and compare strategy easily distinguishes between messages. In addition, it is a straightforward excercise to show that singlemessage security implies manymessage security. 2.1 Constructing a PK encryption system Trapdoor permutations seem to fit the requirements for a public key cryptosystem. We could let the public key be the index i of the function to apply, and the private key be the trapdoor t. Then we might consider Enc(m, i) = f i (m), and Dec(c, i, t) = fi 1 (c). This makes it easy to encrypt, and easy to decrypt with the public key, and hard to decrypt without. Using the RSA function defined in lecture 7, this construction yields the commonly used RSA cryptosystem. However, according to our definition, this construction does not yield a secure encryption scheme. In particular, it is deterministic, so it is subject to comparison attacks. A better scheme (for singlebit messages) is to let Enc(x, i) = {r {0, 1} n : f i (r), b(r) m } 164
5 where b is a hardcore bit for f. This scheme is secure, because distinguishing encryptions of 0 and 1 is essentially the same as recognizing the hardcore bit of a OWP, which we have argued is infeasible. 165
Lecture 10: CPA Encryption, MACs, Hash Functions. 2 Recap of last lecture  PRGs for one time pads
CS 7880 Graduate Cryptography October 15, 2015 Lecture 10: CPA Encryption, MACs, Hash Functions Lecturer: Daniel Wichs Scribe: Matthew Dippel 1 Topic Covered Chosen plaintext attack model of security MACs
More information1 Domain Extension for MACs
CS 127/CSCI E127: Introduction to Cryptography Prof. Salil Vadhan Fall 2013 Reading. Lecture Notes 17: MAC Domain Extension & Digital Signatures KatzLindell Ÿ4.34.4 (2nd ed) and Ÿ12.012.3 (1st ed).
More information1 Message Authentication
Theoretical Foundations of Cryptography Lecture Georgia Tech, Spring 200 Message Authentication Message Authentication Instructor: Chris Peikert Scribe: Daniel Dadush We start with some simple questions
More information1 Construction of CCAsecure encryption
CSCI 5440: Cryptography Lecture 5 The Chinese University of Hong Kong 10 October 2012 1 Construction of secure encryption We now show how the MAC can be applied to obtain a secure encryption scheme.
More information1 Digital Signatures. 1.1 The RSA Function: The eth Power Map on Z n. Crypto: Primitives and Protocols Lecture 6.
1 Digital Signatures A digital signature is a fundamental cryptographic primitive, technologically equivalent to a handwritten signature. In many applications, digital signatures are used as building blocks
More informationLecture 3: OneWay Encryption, RSA Example
ICS 180: Introduction to Cryptography April 13, 2004 Lecturer: Stanislaw Jarecki Lecture 3: OneWay Encryption, RSA Example 1 LECTURE SUMMARY We look at a different security property one might require
More informationLecture 15  Digital Signatures
Lecture 15  Digital Signatures Boaz Barak March 29, 2010 Reading KL Book Chapter 12. Review Trapdoor permutations  easy to compute, hard to invert, easy to invert with trapdoor. RSA and Rabin signatures.
More informationFuzzy IdentityBased Encryption
Fuzzy IdentityBased Encryption Janek Jochheim June 20th 2013 Overview Overview Motivation (Fuzzy) IdentityBased Encryption Formal definition Security Idea Ingredients Construction Security Extensions
More information1 Signatures vs. MACs
CS 120/ E177: Introduction to Cryptography Salil Vadhan and Alon Rosen Nov. 22, 2006 Lecture Notes 17: Digital Signatures Recommended Reading. KatzLindell 10 1 Signatures vs. MACs Digital signatures
More informationIntroduction. Digital Signature
Introduction Electronic transactions and activities taken place over Internet need to be protected against all kinds of interference, accidental or malicious. The general task of the information technology
More informationIdentitybased Encryption with PostChallenge Auxiliary Inputs for Secure Cloud Applications and Sensor Networks
Identitybased Encryption with PostChallenge Auxiliary Inputs for Secure Cloud Applications and Sensor Networks Tsz Hon Yuen  Huawei, Singapore Ye Zhang  Pennsylvania State University, USA Siu Ming
More informationKey Privacy for Identity Based Encryption
Key Privacy for Identity Based Encryption Internet Security Research Lab Technical Report 20062 Jason E. Holt Internet Security Research Lab Brigham Young University c 2006 Brigham Young University March
More informationComputational Soundness of Symbolic Security and Implicit Complexity
Computational Soundness of Symbolic Security and Implicit Complexity Bruce Kapron Computer Science Department University of Victoria Victoria, British Columbia NII Shonan Meeting, November 37, 2013 Overview
More informationTalk announcement please consider attending!
Talk announcement please consider attending! Where: Maurer School of Law, Room 335 When: Thursday, Feb 5, 12PM 1:30PM Speaker: Rafael Pass, Associate Professor, Cornell University, Topic: Reasoning Cryptographically
More informationAuthenticated encryption
Authenticated encryption Dr. Enigma Department of Electrical Engineering & Computer Science University of Central Florida wocjan@eecs.ucf.edu October 16th, 2013 Active attacks on CPAsecure encryption
More informationLecture 9  Message Authentication Codes
Lecture 9  Message Authentication Codes Boaz Barak March 1, 2010 Reading: BonehShoup chapter 6, Sections 9.1 9.3. Data integrity Until now we ve only been interested in protecting secrecy of data. However,
More informationDigital Signatures. Prof. Zeph Grunschlag
Digital Signatures Prof. Zeph Grunschlag (Public Key) Digital Signatures PROBLEM: Alice would like to prove to Bob, Carla, David,... that has really sent them a claimed message. E GOAL: Alice signs each
More informationLecture 5  CPA security, Pseudorandom functions
Lecture 5  CPA security, Pseudorandom functions Boaz Barak October 2, 2007 Reading Pages 82 93 and 221 225 of KL (sections 3.5, 3.6.1, 3.6.2 and 6.5). See also Goldreich (Vol I) for proof of PRF construction.
More informationVictor Shoup Avi Rubin. fshoup,rubing@bellcore.com. Abstract
Session Key Distribution Using Smart Cards Victor Shoup Avi Rubin Bellcore, 445 South St., Morristown, NJ 07960 fshoup,rubing@bellcore.com Abstract In this paper, we investigate a method by which smart
More informationOverview of PublicKey Cryptography
CS 361S Overview of PublicKey Cryptography Vitaly Shmatikov slide 1 Reading Assignment Kaufman 6.16 slide 2 PublicKey Cryptography public key public key? private key Alice Bob Given: Everybody knows
More informationCIS 5371 Cryptography. 8. Encryption 
CIS 5371 Cryptography p y 8. Encryption  Asymmetric Techniques Textbook encryption algorithms In this chapter, security (confidentiality) is considered in the following sense: Allornothing secrecy.
More informationMessage Authentication Code
Message Authentication Code Ali El Kaafarani Mathematical Institute Oxford University 1 of 44 Outline 1 CBCMAC 2 Authenticated Encryption 3 Padding Oracle Attacks 4 Information Theoretic MACs 2 of 44
More informationThe application of prime numbers to RSA encryption
The application of prime numbers to RSA encryption Prime number definition: Let us begin with the definition of a prime number p The number p, which is a member of the set of natural numbers N, is considered
More informationLecture 7: Hashing III: Open Addressing
Lecture 7: Hashing III: Open Addressing Lecture Overview Open Addressing, Probing Strategies Uniform Hashing, Analysis Cryptographic Hashing Readings CLRS Chapter.4 (and.3.3 and.5 if interested) Open Addressing
More informationCryptoVerif Tutorial
CryptoVerif Tutorial Bruno Blanchet INRIA ParisRocquencourt bruno.blanchet@inria.fr November 2014 Bruno Blanchet (INRIA) CryptoVerif Tutorial November 2014 1 / 14 Exercise 1: preliminary definition SUFCMA
More informationMAC. SKE in Practice. Lecture 5
MAC. SKE in Practice. Lecture 5 Active Adversary Active Adversary An active adversary can inject messages into the channel Active Adversary An active adversary can inject messages into the channel Eve
More informationMESSAGE AUTHENTICATION IN AN IDENTITYBASED ENCRYPTION SCHEME: 1KEYENCRYPTTHENMAC
MESSAGE AUTHENTICATION IN AN IDENTITYBASED ENCRYPTION SCHEME: 1KEYENCRYPTTHENMAC by Brittanney Jaclyn Amento A Thesis Submitted to the Faculty of The Charles E. Schmidt College of Science in Partial
More informationMACs Message authentication and integrity. Table of contents
MACs Message authentication and integrity Foundations of Cryptography Computer Science Department Wellesley College Table of contents Introduction MACs Constructing Secure MACs Secure communication and
More informationMTAT.07.003 Cryptology II. Digital Signatures. Sven Laur University of Tartu
MTAT.07.003 Cryptology II Digital Signatures Sven Laur University of Tartu Formal Syntax Digital signature scheme pk (sk, pk) Gen (m, s) (m,s) m M 0 s Sign sk (m) Ver pk (m, s)? = 1 To establish electronic
More informationMessage Authentication Codes 133
Message Authentication Codes 133 CLAIM 4.8 Pr[Macforge A,Π (n) = 1 NewBlock] is negligible. We construct a probabilistic polynomialtime adversary A who attacks the fixedlength MAC Π and succeeds in
More informationAuthentication and Encryption: How to order them? Motivation
Authentication and Encryption: How to order them? Debdeep Muhopadhyay IIT Kharagpur Motivation Wide spread use of internet requires establishment of a secure channel. Typical implementations operate in
More informationLecture 11: The GoldreichLevin Theorem
COM S 687 Introduction to Cryptography September 28, 2006 Lecture 11: The GoldreichLevin Theorem Instructor: Rafael Pass Scribe: Krishnaprasad Vikram HardCore Bits Definition: A predicate b : {0, 1}
More informationMultiInput Functional Encryption for Unbounded Arity Functions
MultiInput Functional Encryption for Unbounded Arity Functions Saikrishna Badrinarayanan, Divya Gupta, Abhishek Jain, and Amit Sahai Abstract. The notion of multiinput functional encryption (MIFE) was
More informationOutline. Computer Science 418. Digital Signatures: Observations. Digital Signatures: Definition. Definition 1 (Digital signature) Digital Signatures
Outline Computer Science 418 Digital Signatures Mike Jacobson Department of Computer Science University of Calgary Week 12 1 Digital Signatures 2 Signatures via Public Key Cryptosystems 3 Provable 4 Mike
More informationDigital Signatures. What are Signature Schemes?
Digital Signatures Debdeep Mukhopadhyay IIT Kharagpur What are Signature Schemes? Provides message integrity in the public key setting Counterparts of the message authentication schemes in the public
More informationCryptography. Jonathan Katz, University of Maryland, College Park, MD 20742.
Cryptography Jonathan Katz, University of Maryland, College Park, MD 20742. 1 Introduction Cryptography is a vast subject, addressing problems as diverse as ecash, remote authentication, faulttolerant
More informationPublic Key Cryptography: RSA and Lots of Number Theory
Public Key Cryptography: RSA and Lots of Number Theory Public vs. PrivateKey Cryptography We have just discussed traditional symmetric cryptography: Uses a single key shared between sender and receiver
More informationPostQuantum Cryptography #4
PostQuantum Cryptography #4 Prof. Claude Crépeau McGill University http://crypto.cs.mcgill.ca/~crepeau/waterloo 185 ( 186 Attack scenarios Ciphertextonly attack: This is the most basic type of attack
More informationLecture 2: Complexity Theory Review and Interactive Proofs
600.641 Special Topics in Theoretical Cryptography January 23, 2007 Lecture 2: Complexity Theory Review and Interactive Proofs Instructor: Susan Hohenberger Scribe: Karyn Benson 1 Introduction to Cryptography
More informationNew Efficient Searchable Encryption Schemes from Bilinear Pairings
International Journal of Network Security, Vol.10, No.1, PP.25 31, Jan. 2010 25 New Efficient Searchable Encryption Schemes from Bilinear Pairings Chunxiang Gu and Yuefei Zhu (Corresponding author: Chunxiang
More informationSecurity Aspects of. Database Outsourcing. Vahid Khodabakhshi Hadi Halvachi. Dec, 2012
Security Aspects of Database Outsourcing Dec, 2012 Vahid Khodabakhshi Hadi Halvachi Security Aspects of Database Outsourcing Security Aspects of Database Outsourcing 2 Outline Introduction to Database
More informationNoninteractive and Reusable Nonmalleable Commitment Schemes
Noninteractive and Reusable Nonmalleable Commitment Schemes Ivan Damgård a Jens Groth b June 16, 2003 Abstract We consider nonmalleable (NM) and universally composable (UC) commitment schemes in the
More informationYale University Department of Computer Science
Yale University Department of Computer Science On Backtracking Resistance in Pseudorandom Bit Generation (preliminary version) Michael J. Fischer Michael S. Paterson Ewa Syta YALEU/DCS/TR1466 October
More informationa Course in Cryptography
a Course in Cryptography rafael pass abhi shelat c 2010 Pass/shelat All rights reserved Printed online 11 11 11 11 11 15 14 13 12 11 10 9 First edition: June 2007 Second edition: September 2008 Third edition:
More informationCryptography. Identitybased Encryption. JeanSébastien Coron and David Galindo. May 15, 2014. Université du Luxembourg
Identitybased Encryption Université du Luxembourg May 15, 2014 Summary IdentityBased Encryption (IBE) What is IdentityBased Encryption? Difference with conventional PK cryptography. Applications of
More information9 Modular Exponentiation and Cryptography
9 Modular Exponentiation and Cryptography 9.1 Modular Exponentiation Modular arithmetic is used in cryptography. In particular, modular exponentiation is the cornerstone of what is called the RSA system.
More informationProofs in Cryptography
Proofs in Cryptography Ananth Raghunathan Abstract We give a brief overview of proofs in cryptography at a beginners level. We briefly cover a general way to look at proofs in cryptography and briefly
More informationCh.9 Cryptography. The Graduate Center, CUNY.! CSc 75010 Theoretical Computer Science Konstantinos Vamvourellis
Ch.9 Cryptography The Graduate Center, CUNY! CSc 75010 Theoretical Computer Science Konstantinos Vamvourellis Why is Modern Cryptography part of a Complexity course? Short answer:! Because Modern Cryptography
More informationIdentitybased encryption and Generic group model (work in progress) Peeter Laud Arvutiteaduse teooriaseminar Tallinn, 05.01.2012
Identitybased encryption and Generic group model (work in progress) Peeter Laud Arvutiteaduse teooriaseminar Tallinn, 05.01.2012 Identitybased encryption Publickey encryption, where public key = name
More informationLecture 2: Universality
CS 710: Complexity Theory 1/21/2010 Lecture 2: Universality Instructor: Dieter van Melkebeek Scribe: Tyson Williams In this lecture, we introduce the notion of a universal machine, develop efficient universal
More informationCryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs
Cryptographic hash functions and MACs Solved Exercises for Cryptographic Hash Functions and MACs Enes Pasalic University of Primorska Koper, 2014 Contents 1 Preface 3 2 Problems 4 2 1 Preface This is a
More informationIntroduction to Cryptography CS 355
Introduction to Cryptography CS 355 Lecture 30 Digital Signatures CS 355 Fall 2005 / Lecture 30 1 Announcements Wednesday s lecture cancelled Friday will be guest lecture by Prof. Cristina Nita Rotaru
More informationCryptography. Lecture Notes from CS276, Spring 2009. Luca Trevisan Stanford University
Cryptography Lecture Notes from CS276, Spring 2009 Luca Trevisan Stanford University Foreword These are scribed notes from a graduate course on Cryptography offered at the University of California, Berkeley,
More informationDIGITAL SIGNATURES 1/1
DIGITAL SIGNATURES 1/1 Signing by hand COSMO ALICE ALICE Pay Bob $100 Cosmo Alice Alice Bank =? no Don t yes pay Bob 2/1 Signing electronically Bank Internet SIGFILE } {{ } 101 1 ALICE Pay Bob $100 scan
More informationLecture 13: Message Authentication Codes
Lecture 13: Message Authentication Codes Last modified 2015/02/02 In CCA security, the distinguisher can ask the library to decrypt arbitrary ciphertexts of its choosing. Now in addition to the ciphertexts
More informationThe Order of Encryption and Authentication for Protecting Communications (Or: How Secure is SSL?)
The Order of Encryption and Authentication for Protecting Communications (Or: How Secure is SSL?) Hugo Krawczyk Abstract. We study the question of how to generically compose symmetric encryption and authentication
More informationChosenCiphertext Security from IdentityBased Encryption
ChosenCiphertext Security from IdentityBased Encryption Dan Boneh Ran Canetti Shai Halevi Jonathan Katz Abstract We propose simple and efficient CCAsecure publickey encryption schemes (i.e., schemes
More informationLecture 13: Factoring Integers
CS 880: Quantum Information Processing 0/4/0 Lecture 3: Factoring Integers Instructor: Dieter van Melkebeek Scribe: Mark Wellons In this lecture, we review order finding and use this to develop a method
More informationSecure Computation Without Authentication
Secure Computation Without Authentication Boaz Barak 1, Ran Canetti 2, Yehuda Lindell 3, Rafael Pass 4, and Tal Rabin 2 1 IAS. E:mail: boaz@ias.edu 2 IBM Research. Email: {canetti,talr}@watson.ibm.com
More informationRSA and Primality Testing
and Primality Testing Joan Boyar, IMADA, University of Southern Denmark Studieretningsprojekter 2010 1 / 81 Correctness of cryptography cryptography Introduction to number theory Correctness of with 2
More informationRSA Encryption. Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles October 10, 2003
RSA Encryption Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles October 10, 2003 1 Public Key Cryptography One of the biggest problems in cryptography is the distribution of keys.
More informationDefinitions for Predicate Encryption
Definitions for Predicate Encryption Giuseppe Persiano Dipartimento di Informatica, Università di Salerno, Italy giuper@dia.unisa.it Thursday 12 th April, 2012 Cryptographic Proofs 1 Content Results on
More informationAdvanced Cryptography
Family Name:... First Name:... Section:... Advanced Cryptography Final Exam July 18 th, 2006 Start at 9:15, End at 12:00 This document consists of 12 pages. Instructions Electronic devices are not allowed.
More informationDepartment Informatik. PrivacyPreserving Email Forensics. Technical Reports / ISSN 21915008. Frederik Armknecht, Andreas Dewald
Department Informatik Technical Reports / ISSN 21915008 Frederik Armknecht, Andreas Dewald PrivacyPreserving Email Forensics Technical Report CS201503 April 2015 Please cite as: Frederik Armknecht,
More informationThreshold Identity Based Encryption Scheme without Random Oracles
WCAN 2006 Threshold Identity Based Encryption Scheme without Random Oracles Jin Li School of Mathematics and Computational Science Sun Yatsen University Guangzhou, P.R. China Yanming Wang Lingnan College
More informationChosenCiphertext Security from IdentityBased Encryption
ChosenCiphertext Security from IdentityBased Encryption Dan Boneh Ran Canetti Shai Halevi Jonathan Katz June 13, 2006 Abstract We propose simple and efficient CCAsecure publickey encryption schemes
More informationCryptography and Network Security Chapter 9
Cryptography and Network Security Chapter 9 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 9 Public Key Cryptography and RSA Every Egyptian received two names,
More informationUniversal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure PublicKey Encryption
Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure PublicKey Encryption Ronald Cramer Victor Shoup December 12, 2001 Abstract We present several new and fairly practical publickey
More informationLecture 17: Reencryption
600.641 Special Topics in Theoretical Cryptography April 2, 2007 Instructor: Susan Hohenberger Lecture 17: Reencryption Scribe: Zachary Scott Today s lecture was given by Matt Green. 1 Motivation Proxy
More informationHierarchical Group Signatures
Hierarchical Group Signatures Mårten Trolin and Douglas Wikström March 22, 2005 Abstract We introduce the notion of hierarchical group signatures. This is a proper generalization of group signatures, which
More informationLeakageResilient Authentication and Encryption from Symmetric Cryptographic Primitives
LeakageResilient Authentication and Encryption from Symmetric Cryptographic Primitives Olivier Pereira Université catholique de Louvain ICTEAM Crypto Group B1348, Belgium olivier.pereira@uclouvain.be
More informationKeywords: Authentication, Third party audit, cloud storage, cloud service provider, Access control.
Volume 5, Issue 3, March 2015 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Identity Based
More information36 Toward Realizing PrivacyPreserving IPTraceback
36 Toward Realizing PrivacyPreserving IPTraceback The IPtraceback technology enables us to trace widely spread illegal users on Internet. However, to deploy this attractive technology, some problems
More informationKey Agreement from Close Secrets over Unsecured Channels Winter 2010
Key Agreement from Close Secrets over Unsecured Channels Winter 2010 Andreas Keller Contens 1. Motivation 2. Introduction 3. Building Blocks 4. Protocol Extractor Secure Sketches (MAC) message authentication
More informationIdentityBased Encryption from the Weil Pairing
Appears in SIAM J. of Computing, Vol. 32, No. 3, pp. 586615, 2003. An extended abstract of this paper appears in the Proceedings of Crypto 2001, volume 2139 of Lecture Notes in Computer Science, pages
More informationCSC474/574  Information Systems Security: Homework1 Solutions Sketch
CSC474/574  Information Systems Security: Homework1 Solutions Sketch February 20, 2005 1. Consider slide 12 in the handout for topic 2.2. Prove that the decryption process of a oneround Feistel cipher
More informationDiscrete Mathematics, Chapter 4: Number Theory and Cryptography
Discrete Mathematics, Chapter 4: Number Theory and Cryptography Richard Mayr University of Edinburgh, UK Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Chapter 4 1 / 35 Outline 1 Divisibility
More information8.1 Makespan Scheduling
600.469 / 600.669 Approximation Algorithms Lecturer: Michael Dinitz Topic: Dynamic Programing: MinMakespan and Bin Packing Date: 2/19/15 Scribe: Gabriel Kaptchuk 8.1 Makespan Scheduling Consider an instance
More informationCryptography and Network Security, PART IV: Reviews, Patches, and11.2012 Theory 1 / 53
Cryptography and Network Security, PART IV: Reviews, Patches, and Theory Timo Karvi 11.2012 Cryptography and Network Security, PART IV: Reviews, Patches, and11.2012 Theory 1 / 53 Key Lengths I The old
More informationTextbook: Introduction to Cryptography 2nd ed. By J.A. Buchmann Chap 12 Digital Signatures
Textbook: Introduction to Cryptography 2nd ed. By J.A. Buchmann Chap 12 Digital Signatures Department of Computer Science and Information Engineering, Chaoyang University of Technology 朝 陽 科 技 大 學 資 工
More informationSYMMETRIC ENCRYPTION. Mihir Bellare UCSD 1
SYMMETRIC ENCRYPTION Mihir Bellare UCSD 1 Syntax A symmetric encryption scheme SE = (K,E,D) consists of three algorithms: K and E may be randomized, but D must be deterministic. Mihir Bellare UCSD 2 Correct
More informationCertificate Based Signature Schemes without Pairings or Random Oracles
Certificate Based Signature Schemes without Pairings or Random Oracles p. 1/2 Certificate Based Signature Schemes without Pairings or Random Oracles Joseph K. Liu, Joonsang Baek, Willy Susilo and Jianying
More informationNetwork Security CS 5490/6490 Fall 2015 Lecture Notes 8/26/2015
Network Security CS 5490/6490 Fall 2015 Lecture Notes 8/26/2015 Chapter 2: Introduction to Cryptography What is cryptography? It is a process/art of mangling information in such a way so as to make it
More informationThe mathematics of cryptology
The mathematics of cryptology Paul E. Gunnells Department of Mathematics and Statistics University of Massachusetts, Amherst Amherst, MA 01003 www.math.umass.edu/ gunnells April 27, 2004 What is Cryptology?
More informationCryptography: RSA and the discrete logarithm problem
Cryptography: and the discrete logarithm problem R. Hayden Advanced Maths Lectures Department of Computing Imperial College London February 2010 Public key cryptography Assymmetric cryptography two keys:
More informationLecture 5  Cryptography
CSE497b Introduction to Computer and Network Security  Spring 2007  Professors Jaeger Lecture 5  Cryptography CSE497b  Spring 2007 Introduction Computer and Network Security Professor Jaeger www.cse.psu.edu/~tjaeger/cse497bs07/
More informationThinking of a (block) cipher as a permutation (depending on the key) on strings of a certain size, we would not want such a permutation to have many
Fixed points of permutations Let f : S S be a permutation of a set S. An element s S is a fixed point of f if f(s) = s. That is, the fixed points of a permutation are the points not moved by the permutation.
More informationSimulationBased Security with Inexhaustible Interactive Turing Machines
SimulationBased Security with Inexhaustible Interactive Turing Machines Ralf Küsters Institut für Informatik ChristianAlbrechtsUniversität zu Kiel 24098 Kiel, Germany kuesters@ti.informatik.unikiel.de
More informationA Proposal for an ISO Standard for Public Key Encryption (version 2.1)
A Proposal for an ISO Standard for Public Key Encryption (version 2.1) Victor Shoup IBM Zurich Research Lab, Säumerstr. 4, 8803 Rüschlikon, Switzerland sho@zurich.ibm.com December 20, 2001 Abstract This
More informationIn this paper a new signature scheme and a public key cryptotsystem are proposed. They can be seen as a compromise between the RSA and ElGamaltype sc
Digital Signature and Public Key Cryptosystem in a Prime Order Subgroup of Z n Colin Boyd Information Security Research Centre, School of Data Communications Queensland University of Technology, Brisbane
More informationQUANTUM COMPUTERS AND CRYPTOGRAPHY. Mark Zhandry Stanford University
QUANTUM COMPUTERS AND CRYPTOGRAPHY Mark Zhandry Stanford University Classical Encryption pk m c = E(pk,m) sk m = D(sk,c) m??? Quantum Computing Attack pk m aka Postquantum Crypto c = E(pk,m) sk m = D(sk,c)
More informationProvableSecurity Analysis of Authenticated Encryption in Kerberos
ProvableSecurity Analysis of Authenticated Encryption in Kerberos Alexandra Boldyreva Virendra Kumar Georgia Institute of Technology, School of Computer Science 266 Ferst Drive, Atlanta, GA 303320765
More informationOutline. Cryptography. Bret Benesh. Math 331
Outline 1 College of St. Benedict/St. John s University Department of Mathematics Math 331 2 3 The internet is a lawless place, and people have access to all sorts of information. What is keeping people
More informationLecture 13. Lecturer: Yevgeniy Dodis Spring 2012
CSCIGA.3210001 MATHGA.2170001 Introduction to Cryptography April 18, 2012 Lecture 13 Lecturer: Yevgeniy Dodis Spring 2012 This lecture is dedicated to constructions of digital signature schemes. Assuming
More informationDigital Signatures. Murat Kantarcioglu. Based on Prof. Li s Slides. Digital Signatures: The Problem
Digital Signatures Murat Kantarcioglu Based on Prof. Li s Slides Digital Signatures: The Problem Consider the reallife example where a person pays by credit card and signs a bill; the seller verifies
More informationA Probabilistic Quantum Key Transfer Protocol
A Probabilistic Quantum Key Transfer Protocol Abhishek Parakh Nebraska University Center for Information Assurance University of Nebraska at Omaha Omaha, NE 6818 Email: aparakh@unomaha.edu August 9, 01
More informationChapter 12. Digital signatures. 12.1 Digital signature schemes
Chapter 12 Digital signatures In the public key setting, the primitive used to provide data integrity is a digital signature scheme. In this chapter we look at security notions and constructions for this
More informationCRYPTOGRAPHY IN NETWORK SECURITY
ELE548 Research Essays CRYPTOGRAPHY IN NETWORK SECURITY AUTHOR: SHENGLI LI INSTRUCTOR: DR. JIENCHUNG LO Date: March 5, 1999 Computer network brings lots of great benefits and convenience to us. We can
More informationCS 758: Cryptography / Network Security
CS 758: Cryptography / Network Security offered in the Fall Semester, 2003, by Doug Stinson my office: DC 3122 my email address: dstinson@uwaterloo.ca my web page: http://cacr.math.uwaterloo.ca/~dstinson/index.html
More information